# How do you multiply #(x+3)(x+4) #?

##### 1 Answer

#### Answer:

#### Explanation:

The rigorous but rather lengthy explanation involves the *distributive law* of multiplication of a sum of two numbers by the third one and *commutative law* for both operations, addition and multiplication.

The *distributive law* of multiplication states:

The *commutative law* of addition states:

The *commutative law* of multiplication states"

All the above laws are used (usually without explicit mentioning) when performing the operations of this problem.

Using the *distributive law* described above for

we obtain:

Now let's use the *commutative law* of multiplication to rewrite it as

Now use the *distributive law* twice, first for

obtaining

and another time for

obtaining

Let's use these equalities in the original expression:

Further simplification involves the following transformations:

Using *commutative* and *distributive* laws,

Obviously,

Our expression looks now as follows:

This is the final representation of the original expression as a polynomial of the second degree.

Of course, most students do all these transformations without even thinking about the laws they are based upon and without writing an intermediary results. But these skills develop as a result of numerous exercises. Practice makes it perfect.